Quandaries
and Queries 

Who is asking: Student Level: Secondary Question: 

Hi Karen, When testing a hypothesis about the mean mu of a population we take a random sample of size n, find the sample mean m and sample standard deviation s and then calculate
A decision is then made about the hypothesis by comparing this number t to number in a table, either a standard normal distribution table or the tdistribution with n1 degrees of freedom. (The choice of distribution depends on the sample size and which book you use.) To test a hypothesis about the standard deviation sigma of a population the procedure is similar but the number you calculate is different and so is the table you use. Again you take a random sample of size n and find the sample standard deviation s. The number you calculate this time is
To make a decision about your hypothesis you compare this number to a critical number as you do for the means test, but the distribution you use in the chisquared distribution with n1 degrees of freedom. Besides having to use a different table, a chisquared table, there is another complication with this test. To apply this test you need to ensure that the population distribution is a normal distribution. I hope this helps, 

